Question

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows: Salary Education 43 7 54 4 ⋮ ⋮ 28 0 Click here for the Excel Data File a. Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round answers to 2 decimal places.) Salaryˆ= Salary ^ = + Education b. Interpret the coefficient for Education. As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590. As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,890. As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $6,890. As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590. c. What is the predicted salary for an individual who completed 6 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.) Salaryˆ Salary ^ $

Salary	Education
43	7
54	4
77	4
53	2
67	5
53	6
114	8
48	0
29	5
50	1
91	9
52	3
59	2
55	5
149	10
51	0
80	9
73	8
135	8
28	0

Answer 1

	Education X	Salary Y	X * Y
	7	43	301	49	1849
	4	54	216	16	2916
	4	77	308	16	5929
	2	53	106	4	2809
	5	67	335	25	4489
	6	53	318	36	2809
	8	114	912	64	12996
	0	48	0	0	2304
	5	29	145	25	841
	1	50	50	1	2500
	9	91	819	81	8281
	3	52	156	9	2704
	2	59	118	4	3481
	5	55	275	25	3025
	10	149	1490	100	22201
	0	51	0	0	2601
	9	80	720	81	6400
	8	73	584	64	5329
	8	135	1080	64	18225
	0	28	0	0	784
Total	96	1361	7933	664	112473

Equation of regression line is


b = 6.89

a =( 1361 - ( 6.8907 * 96 ) ) / 20
a = 34.97
Equation of regression line becomes

As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,890.

When X = 6
= 34.974 + 6.891 X
= 34.974 + 6.891 * 6
= 76.32